Sounds like the longest path problem
. It's a hard problem in the sense of computational complexity - the time it takes to find or approximate the solution grows very quickly with the size of the problem, so solving large instances is not practical in general.
"the longest run in in the cemetery without duplicating any segment and without going through any intersection twice"
reads like a plan to keep the mind occupied (and the result an art form). Had a Diane Rehm podcast on fake news for company today on my straight out & back walk.
BTW, used Strava but haven't a clue how to get its data to AP, ie gpx or fit file hiding somewhere?
In Strava, go to Activity Feed.
Click on title of your run.
In left column, look for wrench icon.
Click on it.
"Export GPX" is then offered as an option.